CN111625986B - Finite element refinement simulation method for shield type earth pressure balance pipe jacking construction - Google Patents
Finite element refinement simulation method for shield type earth pressure balance pipe jacking construction Download PDFInfo
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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- E—FIXED CONSTRUCTIONS
- E21—EARTH DRILLING; MINING
- E21D—SHAFTS; TUNNELS; GALLERIES; LARGE UNDERGROUND CHAMBERS
- E21D9/00—Tunnels or galleries, with or without linings; Methods or apparatus for making thereof; Layout of tunnels or galleries
- E21D9/06—Making by using a driving shield, i.e. advanced by pushing means bearing against the already placed lining
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/13—Architectural design, e.g. computer-aided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads
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- G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
- G06T17/20—Finite element generation, e.g. wire-frame surface description, tesselation
Abstract
The invention discloses a finite element refinement simulation method for shield type earth pressure balance pipe jacking construction, which comprises the following steps: determining the parameter of the shrinkage rate of the pipe piece, wherein the shrinkage rate of the pipe piece comprehensively reflects the stratum loss caused by the functions of heading machine tail gap, grouting friction reduction and soil body disturbance in the pipe jacking construction process; determining the load and construction parameters of pipe jacking construction; determining constitutive models and units adopted by each part during pipe jacking construction simulation; determining the setting of the construction step, wherein the soil body excavation, the heading machine advancing and the segment assembly are realized by the activation and freezing functions of the units, and the stratum loss is realized by the segment shrinkage rate function; and (4) establishing a three-dimensional model by adopting finite element software, and carrying out finite element calculation. The invention comprehensively considers the influence caused by stratum loss caused by the clearance at the tail part of the tunneling machine, grouting antifriction and soil disturbance action, and considers the influence of the constraint action of the tunneling machine and the continuous disturbance action after the top pipe passes through, so that finite element simulation is close to actual construction to the maximum extent.
Description
Technical Field
The invention belongs to the technical field of civil engineering, relates to a numerical simulation technology, and particularly relates to a finite element refined simulation method for shield type earth pressure balance pipe jacking construction.
Technical Field
In recent years, cities have begun to vigorously develop infrastructure construction, particularly utility corridors. In the construction of pipe galleries, pipe jacking construction is the most common, and the method is characterized in that a pipe jacking tunneling machine is gradually pushed into the soil from an originating well to a receiving well by means of jacking equipment such as a jack, and a pipe joint is followed by the pipe joint to finally form a complete channel buried between two working wells. And the rectangular section can improve the space utilization rate and can save about 20% of underground space. However, during the construction process, it is difficult to avoid disturbance of the surrounding soil, which may cause movement of the stratum and deformation of the surrounding structure, and when the pipe jacking is deflected and the tunneling speed is abnormal, the deformation may be further increased, and when the deformation is too large, the damages such as cracking and leakage of the adjacent pipeline, cracking and sinking of the ground, and inclination of the building may occur. It is therefore very necessary to predict the impact of pipe jacking construction on adjacent structures before construction.
The problem of pipe-jacking tunneling is a large-scale three-dimensional nonlinear soil-structure interaction problem, the current finite element method is used as the most common and effective means for researching the problem, and the complicated pipe-jacking tunneling process can be considered, and comprises advancing of a tunneling machine, supporting force of an excavation surface, pipe piece installation, tail grouting and the like. However, in the finite element refinement simulation method for pipe jacking construction of the pipe gallery structure, an equivalent layer method is adopted to replace a grouting layer so as to fill a gap between the tunneling machine and the pipe piece. The simulation mode considers that the influence brought by the weakened grouting layer is equal to the influence brought by stratum loss caused by various factors, and on one hand, the assumption is different from the stratum deformation rule caused by actual construction, and on the other hand, certain difficulty exists in evaluating or acquiring the modulus and the thickness of the equivalent layer. In addition, the modulus of the grouting layer is generally obtained through experience value or field measured data inverse analysis and is a fixed value in the average sense, the equivalent layer represents a mixture of soil and slurry around the tunnel, the value of the modulus of the equivalent layer is related to the soil layer property, and the uniform modulus cannot reflect the characteristic.
Disclosure of Invention
The invention aims to solve the technical problem of providing a finite element refinement simulation method for shield type earth pressure balance pipe jacking construction, and aims to comprehensively consider the influence caused by stratum loss caused by a gap at the tail of a tunneling machine, grouting antifriction and soil disturbance, and consider the influence of the constraint action of the tunneling machine and the continuous disturbance action after pipe jacking crossing, so that finite element simulation is close to actual construction to the maximum extent, and further obtain a simulation result with engineering guidance significance.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a finite element refinement simulation method for shield type earth pressure balance pipe jacking construction is used for simulating the pipe jacking construction process by adopting a finite element method, and comprises the following steps:
determining parameters of segment shrinkage, wherein the segment shrinkage comprehensively reflects stratum loss caused by the functions of heading machine tail gap, grouting friction reduction and soil disturbance in the pipe jacking construction process;
secondly, determining the load and construction parameters of pipe jacking construction;
step three, determining constitutive models and units adopted by each part during pipe jacking construction simulation;
step four, determining the setting of the construction step, wherein the soil body excavation, the heading machine advancing and the segment splicing are realized by the activation and freezing functions of the units, and the stratum loss is realized by the function of setting the segment shrinkage rate;
and step five, establishing a three-dimensional finite element model by adopting finite element software, and performing finite element calculation.
Furthermore, in the first step, the constraint action of the heading machine and the continuous disturbance action after the top pipe passes through need to be considered when the shrinkage rate of the duct piece is determined, and the parameters of the shrinkage rate of the duct piece comprise the constraint length of the heading machine, the shrinkage rate value of the duct piece when no constraint occurs, the shrinkage rate value of the duct piece after continuous disturbance, and the length of the continuous disturbance segment.
Further, the length of the tunneller is constrained, the value of the shrinkage rate of the duct piece when the tunneller is unconstrained, the value of the shrinkage rate of the duct piece after continuous disturbance and the length of the continuous disturbance section are as follows:
the constraint length of the development machine is 1 time of the length of the development machine from the tail part of the development machine to the tail part of the development machine; the shrinkage rate of the duct piece is the void ratio between the development machine and the subsequent duct piece when the duct piece is unconstrained; the shrinkage rate value of the pipe piece after continuous disturbance is 1.5-1.7 times of the void ratio between the tunneling machine and the subsequent pipe piece; the length of the continuous perturbation section is the length of the crossing section.
Furthermore, values of the constraint length, the shrinkage rate value of the duct piece in an unconstrained state, the shrinkage rate value of the duct piece after continuous disturbance and the length of the continuous disturbance section of the heading machine are obtained through inverse analysis according to measured data.
Further, in the second step, the load and construction parameters of the pipe jacking construction comprise jack thrust and tunneling step length; the jack thrust is divided into excavation face supporting force and frictional resistance between the jacking pipe and the surrounding soil body, the frictional resistance has little influence on the surrounding soil body due to grouting antifriction measures and is not simulated, and the excavation face supporting force is determined according to the pressure of the engineering actual measurement soil bin; and the tunneling step length is the width of a single section of jacking pipe.
Furthermore, in the third step, when the pipe jacking construction simulation is carried out, the pipe jacking construction simulation system comprises 4 parts of a soil body, a pipe jacking tunneling machine, a pipe piece and an adjacent structure, and the constitutive models and units adopted by each part are as follows:
soil body: hardening a soil body model and an entity unit by adopting small strain;
pipe-jacking tunneling machine and duct piece: adopting an isotropic linear elastic model and a plate unit;
adjacent structure: the underground pipeline is embedded into the beam unit by adopting an isotropic linear elastic model;
the interaction between the jacking pipe and the soil body is as follows: an interface unit is used.
Further, the small strain hardening soil body model of the soil body has the following calculation parameter values:
stiffness parameters: obtaining a substitution parameter compression index and a substitution parameter rebound index through an indoor test;
strength parameters: determined by geological exploration reports and test results of other literatures;
other parameters refer to the finite element software specification.
Further, in step four, when the construction step is determined, a plurality of groups are defined according to the tunneling step length, specifically as follows:
assuming that the whole tunneling process has N segments of segments, then:
dividing the duct piece into: segment 1, segment 2, … …, segment N;
dividing the interfaces between the pipe and the soil into the following parts according to the tunneling step length: interface 1, interface 2 … …, interface N;
dividing the shrinkage rate of the pipe piece into the following steps according to the tunneling step length: shrink 1, shrink 2 … …, shrink N;
the soil body is divided into the following parts according to the tunneling step length: soil mass 1, soil mass 2, … …, soil mass N;
dividing the supporting force of the excavation surface into: supporting force 1, supporting force 2, … …, and supporting force N;
wherein: changing the material characteristics of the duct piece from a duct piece structure to a heading machine structure when a heading machine is simulated; freezing the soil body and setting the hydraulic condition as dry when simulating soil body excavation;
<1>1, construction step: activating all soil, freezing the pipe jacking structure, the heading machine, the adjacent structure and the supporting force, using K 0 The method makes the initial stress field reach complete balance;
<2> the construction step of No. 2: activating the proximity structure;
<3> No. 3 construction step: freezing the soil body 1; activating a segment 1, an interface 1, a contraction 1 and a supporting force 1;
wherein: the hydraulic condition of the soil body 1 is set as dry; the material of the duct piece 1 is set to be a tunneling machine structure, and the duct piece shrinkage rate of the shrinkage 1 is 0;
and (i) the ith construction step: freezing a soil body i-2 and a supporting force i-3; activating a segment i-2, an interface i-2, a contraction i-2 and a supporting force i-2;
wherein: setting the hydraulic condition of the soil body i-2 as dry; the material of the duct piece i-2 is set to be a heading machine structure, and the shrinkage rate of the duct piece is 0;
<n 1 +2>n th 1 +2 construction step: frozen soil mass n 1 Supporting force n 1 -1; activating segment n 1 Interface n 1 Shrinkage n of 1 And supporting force n 1 ；
Wherein: soil body n 1 The hydraulic conditions of (a) are set to dry; segment n 1 Is arranged as a heading machine structure, contracts n 1 The shrinkage of the tube sheet of (a) is 0;
and (j) the jth construction step: freezing a soil body j-2 and a supporting force j-3; activating a segment j-2, an interface j-2, a contraction j-2 and a supporting force j-2;
wherein: setting the hydraulic condition of the soil body j-2 as dry; the material of the segment j-2 is arranged into a heading machine structure, the segment shrinkage rate of the segment j-2 is 0, and the segment j-2-n 1 The material is arranged into a segment structure and shrinks by 1-j-2-n 1 Shrinkage of tube sheet of (c) ref ＝(j-2-n 1 )×Δc 1 Percent, gradient rate is-delta c 1 Percent/m, the reference plane is the plane where the tail part of the contraction 1 is located;
<2n 1 +2>2n th 1 +2 construction step: frozen soil body 2n 1 Supporting force 2n 1 -1; activating segment 2n 1 2n of the interface 1 2n of shrinkage 1 And supporting force 2n 1 ；
Wherein: 2n of 1 Setting the hydraulic condition of the soil body as dry; segment 2n 1 The material is arranged into a heading machine structure and contracted by 2n 1 The shrinkage of the tube sheet is 0; segment n 1 The material is arranged into a segment structure and shrinks by 1 to n 1 Shrinkage of tube sheet c ref ＝n 1 Δl×Δc 1 Percent, gradient rate is-delta c 1 Percent/m, the reference plane is the plane where the tail part of the contraction 1 is located;
and (k) the kth construction step: freezing a soil body k-2 and a supporting force k-3; activating a segment k-2, an interface k-2, a contraction k-2 and a supporting force k-2;
wherein: setting the hydraulic condition of the soil body k-2 as dry; the duct piece k-2 material is set to be a heading machine structure, and the duct piece shrinkage rate for shrinking k-2 is 0; segment k-2-n 1 The material is arranged into a pipe piece structure and shrinks by k-1-2n 1 ～k-2-n 1 Shrinkage of tube sheet of (c) ref ＝n 1 Δl×Δc 1 Percent, gradient rate is-delta c 1 Percent/m, reference plane is shrinkage k-1-2n 1 The plane of the tail part; shrink 1-k-2-2 n 1 The shrinkage of the tube sheet of (c) ref ＝[n 1 Δl×Δc 1 +(k-2-2n 1 )Δl×Δc 2 ]Percent, gradient rate is-delta c 2 Percent/m, the reference plane is the plane where the tail part of the contraction 1 is located;
<2n 1 +n 2 +2>2n th 1 +n 2 +2 construction step: frozen soil body 2n 1 +n 2 Supporting force 2n 1 +n 2 -1; activating segment 2n 1 +n 2 2n of the interface 1 +n 2 2n of shrinkage 1 +n 2 And supporting force 2n 1 +n 2 ；
Wherein: soil body 2n 1 +n 2 Is set to dry; segment 2n 1 +n 2 The material is arranged into a heading machine structure and contracted by 2n 1 +n 2 The shrinkage of the tube sheet is 0; segment n 1 +n 2 The material is arranged into a pipe piece structure and shrinks by n 2 +1～n 1 +n 2 Shrinkage of tube sheet of (c) ref ＝n 1 Δl×Δc 1 Percent, gradient rate is-delta c 1 % m, reference plane is shrinkage n 2 +1 plane of tail; shrinkage of 1 to n 2 The shrinkage of the tube sheet of (c) ref ＝(n 1 Δl×Δc 1 +n 2 Δl×Δc 2 ) Percent, gradient rate is-delta c 2 Percent/m, the reference plane is the plane where the tail part of the contraction 1 is located;
< N +2> the Nth construction step: freezing a soil body N and a supporting force N-1; activating a segment N, an interface N, a contraction N and a supporting force N;
wherein: setting the hydraulic condition of the soil body N as dry; segment N materialThe material is set to be a heading machine structure, and the shrinkage rate of the segment for shrinking N is 0; segment N-N 1 The material is arranged into a segment structure and shrinks by N +1-2N 1 ～N-n 1 Shrinkage of tube sheet of (c) ref ＝n 1 Δl×Δc 1 Percent, gradient rate is-delta c 1 Percent/m, reference plane is shrinkage N +1-2N 1 The plane of the tail part; shrinking N +1-N 2 -2n 1 ～N-2n 1 Shrinkage of tube sheet of (c) ref ＝(n 1 Δl×Δc 1 +n 2 Δl×Δc 2 ) Percent, gradient rate is-delta c 2 Percent/m, reference plane shrinkage N +1-N 2 -2n 1 The plane of the tail part; shrinkage of 1 to N-N 2 -2n 1 The shrinkage rates of the tube sheets are unified as c ref ＝(n 1 Δl×Δc 1 +n 2 Δl×Δc 2 )％；
<N+3>The N +1 construction step: freezing the supporting force N; segment N +1-N 1 The N material is arranged into a segment structure and shrinks by N +1-N 1 N has a uniform tube sheet shrinkage of c ref ＝n 1 Δl×Δc 1 Percent; shrinking N +1-N 2 -2n 1 ～N-2n 1 Shrinkage of tube sheet of (c) ref ＝(n 1 Δl×Δc 1 +n 2 Δl×Δc 2 ) Percent, gradient rate is-delta c 2 Percent/m, reference plane is shrinkage N +1-N 2 -2n 1 The plane of the tail part; shrinkage of 1 to N-N 2 -2n 1 The shrinkage rates of the tube sheets are unified to c ref ＝(n 1 Δl×Δc 1 +n 2 Δl×Δc 2 )％；
Wherein: the length of a single section is delta l m, and the length of the heading machine is l 1 (n 1 Δ l) m, a cross-over region length of l 2 (n 2 Delta l) m, the void ratio between the development machine and the subsequent segment is c%, and the gradual change rate of the segment shrinkage ratio under the constraint action of the development machine is delta c 1 % m, size (c/l) 1 ) Percent/m, the gradual shrinkage rate of the tube sheet under the action of continuous disturbance is delta c 2 % m, size (0.7 c/l) 2 ) % m, wherein n 1 And n 1 Is a natural number.
Further, in the fifth step, the finite element software adopts Plaxis 3D, and a soil body constitutive model suitable for analyzing the pipe jacking engineering can be provided.
The invention has the beneficial effects that:
(1) the influence of stratum loss caused by a gap at the tail part of the tunneling machine, grouting antifriction and soil disturbance action is comprehensively considered, and the influence of the constraint action of the tunneling machine and the continuous disturbance action after the top pipe passes through on the stratum loss is considered, so that compared with the existing simulation mode, namely the simulation mode of the equivalent stratum, the finite element simulation process is close to the actual top pipe construction process to the maximum extent;
(2) the process of gradually advancing the jacking pipe is simulated in detail, the real physical process of soil body deformation caused by jacking pipe construction can be reflected, and the calculation result can provide certain reference significance for similar projects.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the invention and together with the description serve to explain the invention and not to limit the invention. In the drawings:
FIG. 1 is a flow chart of a finite element refinement simulation method for shield-type earth pressure balance pipe jacking construction according to an embodiment of the present invention;
FIG. 2 is a floor plan and a monitoring point plan provided by an embodiment of the present invention;
FIG. 3 is a geological profile provided by an embodiment of the present invention;
FIG. 4 is a three-dimensional finite element model diagram provided by an embodiment of the present invention;
FIG. 5 is a three-dimensional pipe jacking and adjacent structure model diagram provided by an embodiment of the present invention;
FIG. 6 is a step model diagram of pipe jacking construction (jacking into loop i) according to an embodiment of the present invention;
FIG. 7 is a diagram of a pipe jacking construction step model (jacking ring (i + 1));
FIG. 8 is a comparison graph of the cumulative measured settlement of the sewage pipe measuring point SE on the east side 6 and the sewage pipe measuring point SW on the west side 7 according to the embodiment of the present invention and the variation curve of the calculated settlement along with the tunneling length of the jacking pipe;
FIG. 9 is a comparison graph of the accumulated measured settlement of the east sewage pipe 1 and the calculated settlement versus the variation curve of the pipe jacking tunneling length according to the embodiment of the present invention;
fig. 10 is a comparison graph of the change curve of the accumulated measured settlement of the sewage pipe at the west side 2 and the calculated settlement along with the tunneling length of the jacking pipe according to the embodiment of the present invention.
In the figure: 1. an east sewage pipe; 2. west sewage pipes; 3. a left line pipe jacking; 4. a right line pipe jacking; 5. the heading direction of the jacking pipe; 6. east sewage pipe monitoring point SE; 7. west sewage pipe SW; 8. the contact interface of the jacking pipe and the surrounding soil body; 9. the pipe joint is completed; 10. a pipe-jacking tunneling machine; 11. a supporting force; 12. and (4) soil bodies are not excavated.
Detailed Description
The embodiments of the present invention will be described in further detail with reference to the accompanying drawings, wherein the embodiments and descriptions are only for the purpose of illustrating the invention and are not to be construed as limiting the invention.
Aiming at the defects of a finite element simulation method for pipe-jacking construction in the existing research, the invention provides a finite element refined simulation method for shield-type soil pressure balance pipe-jacking construction, which comprehensively considers the influence caused by stratum loss caused by the gap at the tail part of a tunneling machine, grouting antifriction and soil body disturbance action, and considers the influence of the constraint action of the tunneling machine and the continuous disturbance action after the pipe-jacking passes through on the stratum loss, so that the finite element simulation process is close to the actual pipe-jacking construction process to the maximum extent.
As shown in fig. 1, the present embodiment provides a finite element refinement simulation method for shield-type earth pressure balance pipe jacking construction, which includes the following steps:
determining relevant parameters of the shrinkage rate of a pipe piece, wherein the shrinkage rate of the pipe piece comprehensively reflects the stratum loss rate caused by the effects of heading machine tail gap, grouting antifriction and soil body disturbance in the pipe jacking construction process;
specifically, the most main reason for causing the soil body to move in the pipe jacking construction process is the stratum loss, and the stratum loss is influenced by a plurality of factors and is never the superposition of the influences of all the factors, so that the stratum loss caused by the factors is comprehensively considered by the shrinkage rate of the pipe piece in the finite element simulation. When the shrinkage rate of the duct piece is determined, the constraint action of the tunneling machine and the continuous disturbance action after the top pipe passes through need to be considered, wherein the constraint action of the tunneling machine specifically means that the shrinkage rate of the duct piece is constrained by the boundary of the tunneling machine in front, and the weaker constraint action is along with the farther distance from the tunneling machine, namely the larger shrinkage rate of the duct piece is; the continuous disturbance effect after the top pipe passes through is considered because the pipe joints are gradually pushed into the soil from the starting well in the construction process of the top pipe, namely, the assembled pipe joints can continue to move forward under the action of the jack after the assembly of the pipe pieces is finished, and further continue to influence the surrounding soil or structure, so the constraint effect of the tunneling machine and the continuous disturbance effect after the top pipe passes through are considered to be closer to the actual top pipe construction process. The parameters of the shrinkage rate of the duct piece comprise the constrained length of the development machine, the shrinkage rate value of the duct piece when the development machine is not constrained, the shrinkage rate value of the duct piece after continuous disturbance and the length of the continuous disturbance section.
Further, the length of the tunneller is constrained, the value of the shrinkage rate of the duct piece when the tunneller is unconstrained, the value of the shrinkage rate of the duct piece after continuous disturbance and the length of the continuous disturbance section are as follows:
the constraint length of the development machine is 1 time of the length of the development machine from the tail part of the development machine to the tail part of the development machine; the shrinkage rate of the duct piece is the void ratio between the development machine and the subsequent duct piece when the duct piece is unconstrained; the shrinkage rate value of the duct piece after continuous disturbance is 1.5-1.7 times of the void ratio between the development machine and the subsequent duct piece; the length of the continuous perturbation section is the length of the crossing section.
Furthermore, values of the length of the tunneller in a constrained mode, the shrinkage rate of the duct piece in an unconstrained mode, the shrinkage rate of the duct piece after continuous disturbance and the length of the continuous disturbance section are obtained through inverse analysis according to measured data.
Secondly, determining the load and construction parameters of pipe jacking construction;
specifically, the load and construction parameters of pipe jacking construction comprise jack thrust and tunneling step length; the jack thrust is divided into excavation face supporting force and frictional resistance between the jacking pipe and the surrounding soil body, the frictional resistance has small influence on the surrounding soil body due to grouting antifriction measures and is not simulated, and the excavation face supporting force is determined according to the actually measured pressure of the soil bin in the engineering; by adopting the simulation mode, on one hand, the earth pressure balance in the shield construction process is considered, and the settlement or the uplift of the earth in front of the shield caused by the unbalance of the tunnel face supporting force and the earth pressure in front is avoided; on the other hand, the calculation model is simplified, and finite element calculation is convenient to carry out. The width of a single section of jacking pipe is taken in the tunneling step length, so that the construction step is convenient to set.
Step three, determining constitutive models and units adopted by each part during pipe jacking construction simulation;
specifically, when the pipe jacking construction simulation is carried out, the pipe jacking construction simulation device comprises 4 parts of a soil body, a pipe jacking tunneling machine, a pipe piece and an adjacent structure, and a constitutive model and units adopted by each part are as follows:
soil body: hardening a soil body model and an entity unit by adopting small strain;
pipe-jacking tunneling machine and duct piece: adopting an isotropic linear elastic model and a plate unit;
adjacent structure: the underground pipeline adopts an isotropic linear elastic model and an embedded beam unit;
the interaction between the jacking pipe and the soil body is as follows: an interface unit is used.
Further, the small strain hardening soil body model of the soil body has the following calculation parameter values:
stiffness parameters: obtaining a substitution parameter compression index and a substitution parameter rebound index through an indoor test;
strength parameters: determined by geological exploration reports and test results of other literatures;
other parameters refer to the finite element software specification.
The HSS constitutive model not only considers shear hardening and compression hardening, but also considers the characteristic of small strain stiffness of the soil body, and also increases the consideration of the shear modulus attenuation behavior under the condition of small strain of the soil body, and is further theoretically. Therefore, the HSS constitutive model can be better suitable for soil excavation in a sensitive environment and numerical analysis of surrounding complex environments, the deformation condition can be better predicted by a calculation result, and the HSS constitutive model is considered to be one of the best constitutive models for calculating the pipe jacking project at present.
The embedded beam unit can not only reflect the distance action between the sewage pipe and the soil body, but also simulate the interfacial shearing force between the beam and the soil and follow the coulomb rule related to the normal stress.
Determining the setting of the construction step, wherein during simulation, the excavation of the soil body, the forward construction of the tunneling machine and the assembly of the pipe piece are realized through the activation and freezing functions of the units, and the stratum loss is realized through the function of setting the section shrinkage rate of the pipe piece;
specifically, when the construction step is determined, a plurality of groups are defined according to the tunneling step length, specifically as follows:
assuming that the whole tunneling process has N segments of pipe pieces, then:
dividing the duct piece into: segment 1, segment 2, … …, segment N;
dividing the interfaces between the pipe and the soil into the following parts according to the tunneling step length: interface 1, interface 2 … …, interface N;
and dividing the shrinkage rate of the pipe piece into the following parts according to the tunneling step length: shrink 1, shrink 2 … …, shrink N;
dividing the excavated soil body into: soil mass 1, soil mass 2, … …, soil mass N;
dividing the supporting force of the excavation surface into: supporting force 1, supporting force 2, … …, and supporting force N;
wherein: changing the material characteristics of the duct piece from a duct piece structure to a heading machine structure when a heading machine is simulated; freezing the excavated soil body and setting the hydraulic condition as dry when simulating the excavation of the soil body;
<1>the 1 st construction step: activating all soil bodies, freezing the pipe jacking structure, the heading machine, the adjacent structure and the supporting force, and using K 0 The method makes the initial stress field reach complete balance;
<2> the 2 nd construction step: activating the proximity structure;
<3> No. 3 construction step: freezing the soil body 1; activating a segment 1, an interface 1, a contraction 1 and a supporting force 1;
wherein: the hydraulic condition of the soil body 1 is set as dry; the material of the duct piece 1 is set to be a tunneling machine structure, and the duct piece shrinkage rate of the shrinkage 1 is 0;
and (i) the ith construction step: freezing a soil body i-2 and a supporting force i-3; activating a segment i-2, an interface i-2, a contraction i-2 and a supporting force i-2;
wherein: setting the hydraulic condition of the soil body i-2 as dry; the material of the duct piece i-2 is set to be a heading machine structure, and the shrinkage rate of the duct piece is 0;
<n 1 +2>n th 1 +2 construction step: frozen soil mass n 1 Supporting force n 1 -1; activating segment n 1 Interface n 1 Shrinkage n of 1 And supporting force n 1 ；
Wherein: soil body n 1 The hydraulic conditions of (a) are set to dry; segment n 1 Is arranged as a heading machine structure, contracts n 1 The shrinkage of the tube sheet is 0;
and (j) the jth construction step: freezing a soil body j-2 and a supporting force j-3; activating a segment j-2, an interface j-2, a contraction j-2 and a supporting force j-2;
wherein: setting the hydraulic condition of the soil body j-2 as dry; the material of the segment j-2 is arranged into a structure of a development machine, the shrinkage rate of the segment for shrinking the j-2 is 0, and the segment j-2-n 1 The material is arranged into a segment structure and shrinks by 1-j-2-n 1 Shrinkage of tube sheet of (c) ref ＝(j-2-n 1 )×Δc 1 Percent, gradient rate is-delta c 1 Percent/m, the reference plane is the plane where the tail part of the contraction 1 is located;
<2n 1 +2>2n th 1 +2 construction step: frozen soil body 2n 1 Supporting force 2n 1 -1; activating segment 2n 1 2n of the interface 1 2n of shrinkage 1 And supporting force 2n 1 ；
Wherein: 2n of 1 Setting the hydraulic condition of the soil body as dry; segment 2n 1 The material is arranged into a heading machine structure and contracted by 2n 1 The shrinkage of the tube sheet is 0; segment n 1 The material is arranged into a segment structure and shrinks by 1 to n 1 Shrinkage of tube sheet c ref ＝n 1 Δl×Δc 1 Percent, gradient rate is-delta c 1 Percent/m, the reference plane is the plane where the tail part of the contraction 1 is located;
and (k) the kth construction step: freezing a soil body k-2 and a supporting force k-3; activating a segment k-2, an interface k-2, a contraction k-2 and a supporting force k-2;
wherein: setting the hydraulic condition of the soil body k-2 as dry; the duct piece k-2 material is set to be a heading machine structure, and the duct piece shrinkage rate for shrinking k-2 is 0; segment k-2-n 1 The material is arranged into a pipe piece structure and shrinks by k-1-2n 1 ～k-2-n 1 Shrinkage of tube sheet of (c) ref ＝n 1 Δl×Δc 1 Percent, gradient rate is-delta c 1 Percent/m, reference plane is shrinkage k-1-2n 1 The plane of the tail part; shrink 1-k-2-2 n 1 The shrinkage of the tube sheet of (c) ref ＝[n 1 Δl×Δc 1 +(k-2-2n 1 )Δl×Δc 2 ]Percent, gradient rate is-delta c 2 Percent/m, the reference plane is the plane where the tail part of the contraction 1 is located;
<2n 1 +n 2 +2>2n th 1 +n 2 +2 construction step: frozen soil body 2n 1 +n 2 Supporting force 2n 1 +n 2 -1; activating segment 2n 1 +n 2 2n of the interface 1 +n 2 2n of shrinkage 1 +n 2 And supporting force 2n 1 +n 2 ；
Wherein: soil body 2n 1 +n 2 The hydraulic conditions of (a) are set to dry; segment 2n 1 +n 2 The material is arranged into a heading machine structure and contracted by 2n 1 +n 2 The shrinkage of the tube sheet is 0; segment n 1 +n 2 The material is arranged into a segment structure, and n is shrunk 2 +1～n 1 +n 2 Shrinkage of tube sheet of (c) ref ＝n 1 Δl×Δc 1 Percent, gradient rate is-delta c 1 % m, reference plane is shrinkage n 2 +1 plane of tail; shrinkage of 1 to n 2 The shrinkage of the tube sheet of (c) ref ＝(n 1 Δl×Δc 1 +n 2 Δl×Δc 2 ) Percent, the gradient rate is-delta c 2 Percent/m, the reference plane is the plane where the tail part of the contraction 1 is located;
and (N + 2) the Nth construction step: freezing a soil body N and a supporting force N-1; activating a segment N, an interface N, a contraction N and a supporting force N;
wherein: setting the hydraulic condition of the soil body N as dry; segment N material setting heading machine structureThe shrinkage of the segment of the N shrinkage is 0; segment N-N 1 The material is arranged into a segment structure and shrinks by N +1-2N 1 ～N-n 1 Shrinkage of tube sheet of (c) ref ＝n 1 Δl×Δc 1 Percent, gradient rate is-delta c 1 Percent/m, reference plane is shrinkage N +1-2N 1 The plane of the tail part; shrinking N +1-N 2 -2n 1 ～N-2n 1 Shrinkage of tube sheet of (c) ref ＝(n 1 Δl×Δc 1 +n 2 Δl×Δc 2 ) Percent, gradient rate is-delta c 2 Percent/m, reference plane shrinkage N +1-N 2 -2n 1 The plane of the tail part; shrinkage of 1 to N-N 2 -2n 1 The shrinkage rates of the tube sheets are unified to c ref ＝(n 1 Δl×Δc 1 +n 2 Δl×Δc 2 )％；
<N+3>The N +1 construction step: freezing the supporting force N; segment N +1-N 1 The N material is arranged into a segment structure and shrinks by N +1-N 1 The shrinkage rate of the-N pipe piece is unified as c ref ＝n 1 Δl×Δc 1 Percent; shrinking N +1-N 2 -2n 1 ～N-2n 1 Shrinkage of tube sheet of (c) ref ＝(n 1 Δl×Δc 1 +n 2 Δl×Δc 2 ) Percent, gradient rate is-delta c 2 Percent/m, reference plane is shrinkage N +1-N 2 -2n 1 The plane of the tail part; shrinkage of 1 to N-N 2 -2n 1 The shrinkage rates of the tube sheets are unified to c ref ＝(n 1 Δl×Δc 1 +n 2 Δl×Δc 2 )％；
Wherein: the length of a single section is delta l m, and the length of the heading machine is l 1 (n 1 Δ l) m, a cross-over region length of l 2 (n 2 Delta l) m, the void ratio between the development machine and the subsequent segment is c%, and the gradual change rate of the segment shrinkage ratio under the constraint action of the development machine is delta c 1 % m, size (c/l) 1 ) Percent/m, the gradual shrinkage rate of the tube sheet under the action of continuous disturbance is delta c 2 % m, size (0.7 c/l) 2 ) % m, wherein n 1 And n 1 Is a natural number.
And step five, establishing a three-dimensional finite element model by adopting finite element software, and carrying out finite element calculation.
The finite element software adopts Plaxis 3D, and can provide a soil constitutive model suitable for analyzing the pipe jacking engineering.
Example (b):
the invention is further described below by combining the actual project of pushing and downward passing three sewage main pipes of the comprehensive pipe gallery of the Hangzhou Shangshen route. The plan layout, the monitoring points and the geological section of the project are shown in figures 2 and 3, the three sewage main pipes comprise a sewage pipe on the east side 1 and a sewage pipe on the west side 2, the top pipes are divided into a left top pipe and a right top pipe, namely a left top pipe and a right top pipe, the distance is 3m, the lengths of the top pipes are 106.5m, the length of a single section is 1.5m, the size of the outer contour is 7.5m multiplied by 5.4m, the thickness of the top pipe is 0.55m, and the design strength of the reinforced concrete is C50. The top of the section is buried by 9.8m, the minimum distance between the section and an upper sewage pipe is 4.25m, the inner diameter of the sewage pipe is about 2.2m, and the wall thickness is about 0.22 m.
The size of the tunneling machine adopted for pipe jacking construction is 7.52m multiplied by 5.42m multiplied by 6.2m, and the construction sequence is that 3 left-line pipe jacking is carried out first and 4 right-line pipe jacking is carried out later. In order to monitor the deformation behaviors of the sewage pipe on the east side 1 and the sewage pipe on the west side 2 in the pipe jacking construction process, relevant researches are carried out by taking measuring points above the axis of the left and right pipe jacking, namely a sewage pipe measuring point SE on the east side 6 and a sewage pipe measuring point SW on the west side 7 as examples.
Firstly, determining relevant parameters of the shrinkage rate of the duct piece according to the geometric dimensions of the heading machine and subsequent pipe joints, wherein for simple calculation, the influence range is the multiple of the length of a single section of duct piece, and the method comprises the following specific steps:
the tunneling step length is determined to be 1.5m by the single segment of pipe piece being 1.5m
The constraint length of the development machine is 6m determined by the length of the development machine being 6.2m
The shrinkage rate of the duct piece which is not restricted by the development machine is 0.6 percent determined by the void ratio between the development machine and the subsequent duct piece of 0.6 percent
Determining the length of the continuous disturbance section to be 24m according to the intersection area of the top pipe and the upper sewage pipe to be 25m
The shrinkage rate of the pipe piece after continuous disturbance is determined to be 1.0 percent through back analysis of measured data
Secondly, determining 11 supporting force loads according to actual construction conditions, wherein the bottom supporting force of the tunneling machine is 101.5kPa, and the growth gradient is 6.5 kPa/m.
Thirdly, determining a constitutive model, units and parameters of each part in the model according to the mode in the invention content.
And fourthly, finally, establishing a three-dimensional finite element model for numerical calculation, wherein the three-dimensional finite element model and the structural model diagram are shown in figures 5-6, and the interaction between the jacking pipe and the surrounding soil body is simulated by adopting an 8 jacking pipe and surrounding soil body contact interface unit.
In order to verify the effectiveness of the finite element simulation method, the monitoring data of sewage pipe settlement in the engineering example is combined, and the comparison and analysis are carried out on the monitoring data and the corresponding numerical analysis result, and the change curve of the accumulated settlement of the sewage pipe measuring point SE at the east side 6 and the sewage pipe measuring point SW at the west side 7 along with the tunneling length of the jacking pipe is shown in fig. 8. The comparison graphs of the calculated values and the measured values of all the measuring points of the east and west sewer pipes are shown in fig. 9 to fig. 10.
As can be seen from fig. 8 to 10, the calculated values are closer to the actual measured values, and the finite element model simulation effect is better as a whole, which indicates that the simulation method based on the shrinkage rate of the tube piece can accurately reflect the influence caused by the pipe-jacking construction in consideration of the constraint effect and the continuous disturbance effect of the heading machine.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (7)
1. A finite element refinement simulation method for shield type earth pressure balance pipe jacking construction is characterized by simulating the pipe jacking construction process by adopting a finite element method, and comprises the following steps:
determining parameters of segment shrinkage, wherein the segment shrinkage comprehensively reflects stratum loss caused by a gap at the tail of a tunneling machine, grouting friction reduction and soil disturbance in the pipe jacking construction process, the constraint action of the tunneling machine and the continuous disturbance action after the pipe jacking passes through need to be considered when the segment shrinkage is determined, the parameters of the segment shrinkage include the constraint length of the tunneling machine, the value of the segment shrinkage when no constraint is performed, the value of the segment shrinkage after continuous disturbance, and the length of the continuous disturbance segment, and the constraint length of the tunneling machine is 1 time of the length of the tunneling machine from the tail of the tunneling machine to the tail of the tunneling machine; the shrinkage rate of the duct piece is the void ratio between the development machine and the subsequent duct piece when the duct piece is unconstrained; the shrinkage rate value of the pipe piece after continuous disturbance is 1.5-1.7 times of the void ratio between the tunneling machine and the subsequent pipe piece; the length of the continuous disturbance section is the length of the crossing section;
determining the load and construction parameters of pipe jacking construction, wherein the load and construction parameters of the pipe jacking construction comprise jack thrust and tunneling step length;
step three, determining constitutive models and units adopted by each part during pipe jacking construction simulation, wherein the pipe jacking construction simulation comprises 4 parts of a soil body, a pipe jacking tunneling machine, a pipe piece and an adjacent structure;
step four, determining the setting of the construction step, wherein the soil body excavation, the heading machine advancing and the segment splicing are realized by the activation and freezing functions of the units, and the stratum loss is realized by the function of setting the segment shrinkage rate;
and step five, establishing a three-dimensional finite element model by adopting finite element software, and carrying out finite element calculation.
2. The finite element refinement simulation method for shield-type earth pressure balance pipe jacking construction according to claim 1, characterized in that: and the length of the heading machine is restrained, the shrinkage rate value of the duct piece when the heading machine is not restrained, the shrinkage rate value of the duct piece after continuous disturbance and the length value of the continuous disturbance section are obtained by inverse analysis according to the measured data.
3. The finite element refinement simulation method for shield-type earth pressure balance pipe jacking construction according to claim 1, characterized in that: in the second step, the thrust of the jack is divided into an excavation surface supporting force and frictional resistance between the jacking pipe and the surrounding soil body, the frictional resistance has little influence on the surrounding soil body due to grouting antifriction measures and is not simulated, and the excavation surface supporting force is determined according to the pressure of the engineering actual measurement soil bin; and the tunneling step length is the width of a single section of jacking pipe.
4. The finite element refinement simulation method for shield-type earth pressure balance pipe jacking construction according to claim 1, characterized in that: in the third step, when the pipe jacking construction simulation is carried out, the constitutive models and units adopted by each part are as follows:
soil body: hardening a soil body model and an entity unit by adopting small strain;
pipe-jacking tunneling machine and duct piece: adopting an isotropic linear elastic model and a plate unit;
adjacent structure: the underground pipeline adopts an isotropic linear elastic model and an embedded beam unit;
the interaction between the jacking pipe and the soil body is as follows: an interface unit is used.
5. The finite element refinement simulation method for shield-type earth pressure balance pipe jacking construction according to claim 4, wherein the finite element refinement simulation method comprises the following steps: the small strain hardening soil body model of the soil body has the following calculation parameter values:
stiffness parameters: obtaining a substitution parameter compression index and a substitution parameter rebound index through an indoor test;
strength parameters: determined by geological exploration reports and test results of other literatures;
other parameters refer to the finite element software specification.
6. The finite element refinement simulation method for shield-type earth pressure balance pipe jacking construction according to claim 1, characterized in that: in the fourth step, when the construction step is determined, a plurality of groups are defined according to the tunneling step length, specifically as follows:
assuming that the whole tunneling process has N segments of segments, then:
dividing the duct piece into: segment 1, segment 2, … …, segment N;
dividing the interface between the pipe and the soil into: interface 1, interface 2 … …, interface N;
and dividing the shrinkage rate of the pipe piece into the following parts according to the tunneling step length: shrink 1, shrink 2 … …, shrink N;
the soil body is divided into the following parts according to the tunneling step length: soil mass 1, soil mass 2, … …, soil mass N;
dividing the supporting force of the excavation surface into: supporting force 1, supporting force 2, … …, and supporting force N;
wherein: changing the material characteristics of the duct piece from a duct piece structure to a heading machine structure when a heading machine is simulated; freezing the soil body and setting the hydraulic condition as dry when simulating soil body excavation;
<1>the 1 st construction step: activating all soil, freezing the pipe jacking structure, the heading machine, the adjacent structure and the supporting force, using K 0 The method makes the initial stress field reach complete balance;
<2> the construction step of No. 2: activating the proximity structure;
<3> No. 3 construction step: freezing the soil body 1; activating a segment 1, an interface 1, a contraction 1 and a supporting force 1;
wherein: the hydraulic condition of the soil body 1 is set as dry; the material of the duct piece 1 is set to be a tunneling machine structure, and the duct piece shrinkage rate of the shrinkage 1 is 0;
and (i) the ith construction step: freezing a soil body i-2 and a supporting force i-3; activating a segment i-2, an interface i-2, a contraction i-2 and a supporting force i-2;
wherein: setting the hydraulic condition of the soil body i-2 as dry; the material of the duct piece i-2 is set to be a heading machine structure, and the shrinkage rate of the duct piece is 0;
<n 1 +2>n th 1 +2 construction step: frozen soil mass n 1 Supporting force n 1 -1; activating segment n 1 Interface n 1 Shrinkage n of 1 And supporting force n 1 ；
Wherein: soil body n 1 The hydraulic conditions of (a) are set to dry; segment n 1 Is arranged as a heading machine structure, contracts n 1 The shrinkage of the tube sheet is 0;
and (j) the jth construction step: freezing a soil body j-2 and a supporting force j-3; activating a segment j-2, an interface j-2, a contraction j-2 and a supporting force j-2;
wherein: setting the hydraulic condition of the soil body j-2 as dry; the material of the segment j-2 is arranged into a structure of a development machine, the shrinkage rate of the segment for shrinking the j-2 is 0, and the segment j-2-n 1 The material is arranged into a segment structure and shrinks by 1-j-2-n 1 OfThe shrinkage rate of the film is reduced,c ref =（j-2-n 1 ）×Δc 1 % of gradient is-deltac 1 Percent/m, the reference plane is the plane where the tail part of the contraction 1 is located;
<2n 1 +2>2n th 1 +2 construction step: frozen soil body 2n 1 Supporting force 2n 1 -1; activating segment 2n 1 2n of the interface 1 2n of shrinkage 1 And supporting force 2n 1 ；
Wherein: 2n of 1 Setting the hydraulic condition of the soil body as dry; segment 2n 1 The material is arranged into a heading machine structure and contracted by 2n 1 The shrinkage of the tube sheet is 0; segment n 1 The material is arranged into a segment structure and shrinks by 1-n 1 Shrinkage of tube sheetc ref =n 1 Δl×Δc 1 % of gradient is-deltac 1 Percent/m, the reference plane is the plane where the tail part of the contraction 1 is located;
and (k) the kth construction step: freezing a soil body k-2 and a supporting force k-3; activating a segment k-2, an interface k-2, a contraction k-2 and a supporting force k-2;
wherein: setting the hydraulic condition of the soil body k-2 as dry; the duct piece k-2 material is set to be a heading machine structure, and the duct piece shrinkage rate for shrinking k-2 is 0; segment k-2-n 1 The material is arranged into a pipe piece structure and shrinks by k-1-2n 1 ~k-2-n 1 The shrinkage rate of the tube sheet of (a),c ref =n 1 Δl×Δc 1 % of gradient is-deltac 1 Percent/m, reference plane is shrinkage k-1-2n 1 The plane of the tail part; shrinkage of 1 to k-2-2n 1 The shrinkage rate of the tube sheet of (a),c ref =[n 1 Δl×Δc 1 +（k-2-2n 1 ）Δl×Δc 2 ]% of gradient is-deltac 2 Percent/m, the reference plane is the plane where the tail part of the contraction 1 is located;
<2n 1 +n 2 +2>2n th 1 +n 2 +2 construction step: frozen soil body 2n 1 +n 2 Supporting force 2n 1 +n 2 -1; activating segment 2n 1 +n 2 2n interface 1 +n 2 2n of shrinkage 1 +n 2 And supporting force 2n 1 +n 2 ；
Wherein: soil body 2n 1 +n 2 The hydraulic conditions of (a) are set to dry; segment 2n 1 +n 2 The material is arranged into a heading machine structure and contracted by 2n 1 +n 2 The shrinkage of the tube sheet is 0; segment n 1 +n 2 The material is arranged into a segment structure, and n is shrunk 2 +1~n 1 +n 2 The shrinkage rate of the tube sheet of (a),c ref =n 1 Δl×Δc 1 % of gradient is-deltac 1 % m, reference plane is shrinkage n 2 +1 plane of tail; shrinkage of 1 to n 2 The shrinkage rate of the tube sheet of (a),c ref =（n 1 Δl×Δc 1 +n 2 Δl×Δc 2 ) % of gradient is-deltac 2 Percent/m, the reference plane is the plane where the tail part of the contraction 1 is located;
< N +2> the Nth construction step: freezing a soil body N and a supporting force N-1; activating a segment N, an interface N, a contraction N and a supporting force N;
wherein: setting the hydraulic condition of the soil body N as dry; the duct piece N material is set to be a heading machine structure, and the duct piece shrinkage rate for shrinking N is 0; segment N-N 1 The material is arranged into a segment structure and shrinks by N +1-2N 1 ~N-n 1 The shrinkage rate of the tube sheet of (a),c ref =n 1 Δl×Δc 1 % of gradient is-deltac 1 Percent/m, reference plane is shrinkage N +1-2N 1 The plane of the tail part; shrinking N +1-N 2 -2n 1 ~N-2n 1 The shrinkage rate of the tube sheet of (a),c ref =（n 1 Δl×Δc 1 +n 2 Δl×Δc 2 ) % of gradient is-deltac 2 Percent/m, reference plane shrinkage N +1-N 2 -2n 1 The plane of the tail part; shrinkage of 1 to N-N 2 -2n 1 The shrinkage rates of the pipe pieces are unified toc ref =（n 1 Δl×Δc 1 +n 2 Δl×Δc 2 ）%；
<N+3>The N +1 construction step: freezing the supporting force N; pipeSlice N +1-N 1 Setting N material as a segment structure, and shrinking N +1-N 1 N is the uniform shrinkage of the tube sheetc ref =n 1 Δl×Δc 1 Percent; shrinking N +1-N 2 -2n 1 ~N-2n 1 The shrinkage rate of the tube sheet of (a),c ref =（n 1 Δl×Δc 1 +n 2 Δl×Δc 2 ) % of gradient is-deltac 2 Percent/m, reference plane is shrinkage N +1-N 2 -2n 1 The plane of the tail part; shrinkage of 1 to N-N 2 -2n 1 The shrinkage rates of the pipe pieces are unified toc ref =（n 1 Δl×Δc 1 +n 2 Δl×Δc 2 ） %；
Wherein: length of single segment is deltalm, the length of the development machine isl 1 （n 1 Δl) m, the length of the crossing region isl 2 （n 2 Δl) m, the void ratio between the development machine and the subsequent duct piece iscPercent, the gradual change rate of the shrinkage rate of the pipe piece under the constraint action of the tunneling machine is deltac 1 % m, size: (c/l 1 ) Percent/m, the gradual change rate of the tube sheet shrinkage under the action of continuous disturbance is deltac 2 % m, size (0.7)c/l 2 ) % m, wherein n 1 And n 1 Is a natural number.
7. The finite element refinement simulation method for shield-type earth pressure balance pipe jacking construction according to claim 1, characterized in that: and step five, adopting Plaxis 3D as finite element software.
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| US4966494A (en) * | 1987-12-09 | 1990-10-30 | Kurimoto Ltd. | Low load pipe for pipe jacking |
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| US4966494A (en) * | 1987-12-09 | 1990-10-30 | Kurimoto Ltd. | Low load pipe for pipe jacking |
| JP2012158923A (en) * | 2011-02-01 | 2012-08-23 | Tokyo Electric Power Co Inc:The | Small-diameter pipe jacking method |
| CN110245426A (en) * | 2019-06-17 | 2019-09-17 | 中铁七局集团有限公司 | A kind of finite element fining analogy method for Pipe rack jacking construction |
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